Prove that Composite Function with Inverse is x itself

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Function machine relates input to output with a well defined rule. Composite functions are functions of functions. Operations of the inside function are performed and the outside function. All the operations are performed in an order. Function notation is used to represent output y as g(x) for input x.

[MathematicsTutor]

Good example to understand steps to find inverse of Rational Function

[neilfairbairn]

Not a proof but thanks for the example